The Arrow in the Law: Emergent Gravity from a Discrete, Irreversible Substrate

Modern physics puts time-symmetric laws at the foundation and explains the arrow of time as a contingent fact about boundary conditions — the universe simply started in a low-entropy state. This paper develops the opposite hypothesis: that the most fundamental thing about the world is not a symmetric equation but an irreversible act of becoming, so that the arrow of time is written into the law itself. It then asks the sharpest possible test of that idea — what theory of gravity does such a substrate produce? — and follows the answer all the way to simulation. The result is that a discrete, relational substrate whose only special feature is irreversibility reproduces the architecture of general relativity. A Lorentzian metric emerges as the coarse-grained shadow of a "bandwidth" field; the weak-field limit is Einstein's, including the factor-of-two light deflection that decided the 1919 eclipse; and the full theory is not quite General Relativity but khronometric gravity — Einstein's two gravitational-wave modes plus one extra scalar. That scalar turns out to be the arrow of time itself, made dynamical. A single structural fact organizes everything: the same irreversibility selects the Einstein branch of the metric, promotes the extra mode from gauge to physical, and pins it to the speed of light. One idea, three consequences. The emergent field equation forms black-hole horizons spontaneously, and they carry area-law entropy and a Hawking-like temperature. The paper is offered as a worked example of a generative substrate ontology yielding the structure of gravity with a single, falsifiable departure. It is scrupulously tiered: every claim is marked as derived, measured, structural, inherited from observation, or open — and where a number cannot yet be computed honestly (the preferred-frame parameters, the magnitude of the cosmological constant), it is named and not fabricated. The theory can lose, and the paper marks exactly where. Whether or not the universe is built this way, the construction shows that "the arrow of time is fundamental" is not idle metaphysics but a productive hypothesis with specific, derivable, and in places falsifiable consequences for the form of gravity.